gohenathaon -- I will forgive (or drop the last a, so, gohenathon?)
gohenathach -- you will forgive
gohenatha -- he/she/it will forgive
gohenatham -- we will forgive
gohenathech -- you will forgive
gohenathar -- they will forgive

Am I anywhere close?

Also, I'm confused by pronoun use, specifically, when a pronoun should be combined with a verb for the speaker, or how they can be used as objects?

If I wanted to say: "I forgive you"

Gohenan le -- I forgive thee? or
Im gohenach -- I you forgive?

Or, more likely, something completely different?

Would it be different if you used a proper name instead of "you?" Is "Gohenan John" proper for "I forgive John?"

Re: Conjugation and pronouns?

Definitely not gohenal; -l is a Quenya second-person ending. As for singular versus plural, I think that -ch has been accepted to cover both, post-movie.

gohenathaon -- I will forgive (or drop the last a, so, gohenathon?)

Should be gohenathon: the first-person ending -n always forces the -a to umlaut to -o-.

gohenathech -- you will forgive

Should also be gohenathach.

Everything else looks good.

As for pronouns -- the ending added to the verb indicates the subject of the sentence, and a pronoun is used as the object. Between your two examples, Gohenon le (note the spelling) would be the correct construction. And yes, you can replace the pronoun with any noun as the object of a verb -- but keep in mind that a noun used as an object will have its initial consonant lenited.